About the possible interpretation of this effect, if confirmed, I would like to point out that a plane wave implies a modified metric in general relativity. This has been presented in Misner, Thorne, Wheeler, Gravitation at section 35.11 page 961. You can also find a Wikipedia entry describing it. For the article used in the measurements the situation is more involved as the frustum has not just a single mode but, in principle, each one of these can be seen as propagating in a modified metric. The smaller the input power the smaller the effect. It is my conviction that a full understanding could be achieved with a proper treatment using general relativity. What I have found in literature is overlooking any analysis of the interaction between microwaves and space-time. The effect is miniscule in any case but the interferometer devised at Eagleworks seems well equipped to unveil it.

Concerning obtaining the frequency and mode shape, does your University give you access to a Finite Element analysis package like COMSOL, or ANSYS Multiphysics, etc. so that you could then obtain a numerical solution for any arbitrary geometry and inserted dielectric ?

For those of us who are not in a position to built a test device, it would be fantastic to play around with a simulation. Cherry on the cake: make it available on github, and link it from the created-a-moment-ago wiki.

Oh, I forgot: if the 3D model would be made with, say, openSCAD (http://www.openscad.org/) then we could parametrize it easily and 3D print it as a shelf model to look at while waiting for the FE simulations to complete...

He might have more experience with it than I. I would guess you can increase the surface of the capacitor to increase your sensitivity. A lock-in amplifier can eliminate noise and amplifiers can further amplify the signal from the capacitor. It is an alternative to other ways of measuring. I'm wondering if there might be a way to tune the rate of natural osculation of the system by applying a small offset DC voltage (of the AC wave to used to measure capacitance) as a way of tuning. There might be some give and take compared to other methods. I haven't ever personally used one.

I do not think it will have constant acceleration for constant power input over time, because the matter of the frustum and it's source will experience relativistic effects, on mass, time and length. It takes more than a frustum to make an actual warp drive.

...

Question: under your interpretation, the Emdrive would have a maximum speed always less than c, because acceleration would eventually decrease until maybe becoming zero due to relativistic effects on the frustum at some speed. Is that correct?

If so, what speed are we talking about? something close to c or much lower?

This topic of the Emdrive's maximum speed and the potentially diminishing acceleration is something that has appeared repeatedly in the discussions, without a clear answer yet because there is no experimental data backing it or disproving it yet.

This notion has also been rebuffed by some people, because assuming a "maximum speed" also assumes a privileged reference frame, which is a big no no in current theories.

I feel there could be a GR explanation, related to the fact that we do have an absolute speed limit: the speed of light, which is the same on all reference frames, including that of the microwaves inside the frustum.

The reason some people mentioned reduced acceleration at higher velocities, is with classic newtonian thrust, kinetic energy is squared to the speed. EM Drive tech is by some assumed to convert electrical energy directly to kinetic energy (or at least using a different mechanism than action/reaction), which is a linear process. By that statement alone, you can deduce that with constant power input, and not taking into account relativistic effects, the acceleration will reduce, but it will not do so asymptotically. It's a square root. Of course it will force itself into an asymptote because of eventual relativistic effects (For the distant observer). From traveller's PoV, you can still accellerate indefinitely and the traveller's perceived speed can still go to infinity. Relativity is still in tact as a whole.

He might have more experience with it than I. I would guess you can increase the surface of the capacitor to increase your sensitivity. A lock-in amplifier can eliminate noise and amplifiers can further amplify the signal from the capacitor. It is an alternative to other ways of measuring. I'm wondering if there might be a way to tune the rate of natural osculation of the system by applying a small offset DC voltage (of the AC wave to used to measure capacitance) as a way of tuning. There might be some give and take compared to other methods. I haven't ever personally used one.

That was an MIT gizmo, a balanced system of a differential transformer and 4 capacitor plates into which one placed a grounded vane. Because it was an AC bridge circuit it easily measured microinches, and that wasn't pushing it at all.

Edit: It would not be too hard to modify this into a unit that would both measure displacement and supply a restoring force.

About the possible interpretation of this effect, if confirmed, I would like to point out that a plane wave implies a modified metric in general relativity. This has been presented in Misner, Thorne, Wheeler, Gravitation at section 35.11 page 961. You can also find a Wikipedia entry describing it. For the article used in the measurements the situation is more involved as the frustum has not just a single mode but, in principle, each one of these can be seen as propagating in a modified metric. The smaller the input power the smaller the effect. It is my conviction that a full understanding could be achieved with a proper treatment using general relativity. What I have found in literature is overlooking any analysis of the interaction between microwaves and space-time. The effect is miniscule in any case but the interferometer devised at Eagleworks seems well equipped to unveil it.

Thanks for the reference and the excellent comment.

This analysis seems very difficult to perform. The plane wave is a mathematical idealization: it is not possible in practice to have a true plane wave; only a wave of infinite extent will propagate as a plane wave. Far away from an antenna, it may be a good approximation, but I think you will agree, not inside the small and finite truncated cone (fustrum) used for the EM Drive which is a closed cavity with practically perfectly reflecting walls.

The plane wave solution is one of the few exact solutions in general relativity ( https://en.wikipedia.org/wiki/Category:Exact_solutions_in_general_relativity ). I doubt whether it is possible to obtain an exact solution for waves in the truncated cone using general relativity. Even using just Maxwell's equations, the solution for the truncated cone involves two separate eigenvalue problems that need to be solved numerically (one eigenvalue problem in terms of associated Legendre functions and another eigenvalue problem in terms of spherical Bessel functions).

How is one to proceed?

I see your point, that each mode propagates in a modified metric, but how do we analyze this effect inside the geometry of the truncated cone? And like you state, the effect should be miniscule, so I don't understand how this effect will produce a thrust force measurement (for the same power input) that is thousands of times greater than the one of a perfectly collimated photon rocket (letting all the photons escape out of the drive perfectly parallel to each other).

The EM Drive will sit on top of but not connected to one end of a balance beam. On the other will be an adjustable counter balance mass. Very low stiction bearings will be used.

The EM Drive end of the balance beam will sit on top of but not connected to a digital load cell with a 0.01g resolution / 0.5kg max and be connected via USB to a laptop running data logger software. Would like more resolution, will see how the budget goes.

The counter balance will be adjusted to produce a down force on the load cell of 0.25kg when the EM Drive is unpowered so to bias the load cell into the middle of it's range.

The frequency and power adjustable RF source will be connected to the EM Drive by a free floating length of coax with SWR matching capability and to the laptop via USB connector. Control of frequency and power will be via software on the laptop.

The idea is to keep this KISS and stay as close to the 1st Shawyer test setup that also used vertical orientation of the EM Drive.

Based on achieving 10mN/kW (~1gf/kW) performance, the desired 0.1gf (10x load cell resolution) will need the application of 100W of RF power.

Desire is to use common 2.4GHz narrow band WiFi based signal generators which can be smoothly varied in frequency and power output to find optimal cavity frequency and energy loading.

As this is a narrow band RF signal, ideally the end caps should be spherical to eliminate end plate variable phase change and to get a much better cavity Q. But being a realist and KISS engineer, who hates to reinvent the wheel, will start with simpler flat plates and will follow the excellent work of Mullerton.

TheTraveler, the RF generator/amplifier/etc could be placed on the scale as part of the counter weight, no floating RF cables this way. Power supply could come up from the center.

There is also need for a down pointing arm from center with a weight for stability.

This setup should not be affected by buckling.

RF gen & wide band RF amp need pwr and USB connections. Probably better to feed a single & thin RF cable up through a hole in the teeter totter centre and then to left side EM Drive but leave the electronics on the bench.

The balance beam will be at least 200mm wide (bit wider than EM Drive external support rods), with through axle & 2 side bearings, so should be no stability issues. Design like kids teeter totter. Simple. KISS.

Roger no thermal buckling or CG movement issues.

The 4 EM Drive external rod supports will sit on one end on the Teeter Totter. Sorry girls I need your Teeter Totter.

Yes but only when observed from a reference frame. Traveller's accelleration (from travellers PoV) reduces as a square root and that is not asymptotically (the limit you stated). If it were, speed from the traveller's frame of reference could never grow toward infinity, which it can occording to GR.

TheTraveler, the RF generator/amplifier/etc could be placed on the scale as part of the counter weight, no floating RF cables this way. Power supply could come up from the center.

There is also need for a down pointing arm from center with a weight for stability.

This setup should not be affected by buckling.

RF gen & wide band RF amp need pwr and USB connections. Probably better to feed a single & thin RF cable up through a hole in the teeter totter centre and then to left side EM Drive but leave the electronics on the bench.

The balance beam will be at least 200mm wide (bit wider than EM Drive external support rods), with through axle & 2 side bearings, so should be no stability issues. Design like kids teeter totter. Simple. KISS.

Roger no thermal buckling or CG movement issues.

The 4 EM Drive external rod supports will sit on one end on the Teeter Totter. Sorry girls I need your Teeter Totter.

I do not think it will have constant acceleration for constant power input over time, because the matter of the frustum and it's source will experience relativistic effects, on mass, time and length. It takes more than a frustum to make an actual warp drive.

For now, I'm not certain that having the resonance occur inside the frustum is necessary. Resonance could occur in an exterior chamber, like pumping a "laser", something to pump the input power. Then inject a tuned coherent pulse of limited bandwidth into the frustum near it's cut-off modes. The objective being, to use the variable refractive index to amplify the momentum toward the small end. By this I mean, the momentum transforms due to the refractive index,

p => p*sqrt(c/vg)

The group velocity depends on location in the frustum and is lowest at the small end. So momentum is amplified toward the small end. The energy is not lost through resistive copper losses, it is absorbed through momentum transfer of the exponentially decaying waves that have been squeezed beyond their cut-off diameter in the waveguide. For these waves, the speed of light has come to a halt and they cannot propagate, so their momentum must be absorbed by the frustum. Where else can it go? They have crossed the event horizon, where c -> 0, the momentum can't escape.

The resonant modes are probably not so close to the cut-off and contribute very little, if anything. There is still a gradient in v group, but a much, much smaller one. I would consider this a different design, one that optimizes Q and very high energy storage over thrust, but the result will work for the same reason.

You also asked me for some equations, graphs and such. I've just started researching here and found an enormous body of information I did not know about. So... it may be a while. Any questions you may have on the PV Model and my quantum electrodynamic interpretation of it, I'm happy to assist.

Best Regards,Todd D.

Todd,

It is exciting to read your explanation about exponentially decaying waves that have been squeezed beyond their cut-off diameter in the waveguide. You write very clearly.

It is shown that all modes run continuously from travelling waves through a transition to an evanescent (exponentially decaying) wave region and the value of the attenuation increases as they approach the cone vertex.

One mode after the other reaches cutoff in the tapered hollow metallic waveguide as they approach the cone vertex.

Unfortunately, this analysis is for an open waveguide, not for a closed cavity, but the fact that a strict distinction between pure travelling waves and pure evanescent waves cannot be achieved for a conical waveguide, also has implications for modes approaching cutoff in the truncated cone cavity.

ADDENDUM:

One thing that has not been explored is whether these truncated cones are being prematurely ended towards the cone vertex. The tested designs are almost cylindrical.

Roger Shawyer has progressively (but very slowly with time) increased the cone angle of his truncated cones, culminating in the superconducting design he unveiled last October 2014. NASA Eagleworks and Yang in China have truncated cone designs that look like earlier Shawyer designs, with smaller cone angles.

For reference. the tangent of the cone's half angle thetaw and the cone's half angle thetaw, in ascending order, for the following cases are:

(Notice how Shawyer progressively increased the cone's half-angle, with time, in his experimental designs, by a factor of 7 in the tangent of the half-angle)

The people looking at running experiments here are (understandably) also looking at earlier designs with small cone angles and prematurely terminated before reaching the vertex. The group from a university was looking at running experiments with perfectly cylindrical geometry.

Given the latest write-up by Shawyer (concerning his choice of R1 being too large) it appears that what you are bringing up concerning modes near cutoff has not yet been appreciated or explored, as the researchers are not focusing on general wave solutions in the complex plane containing simultaneously both real and imaginary components.

Best regards,

PS: @aero has valiantly attempted to run a full analysis, of general waves, containing simultaneously both real and imaginary components, using MEEP. Unfortunately MEEP is finite difference code and hence he has only been able to run 2-D simulations (due to computer time limitations). It is known that this problem (truncated cone) is 3-D, as a 2-D analysis cannot simulate very important features of the geometry. The MEEP solutions have also been very difficult to interpret, because of the lack of suitable post-processing software to explore the solutions.

@Mulletron envisioned a completely conical EM Drive, terminating at the vertex (at the beginning of the thread when we were all trying to explore all possibilities with an open mind). A perfect cone may not be the best solution because in a perfect cone ALL modes are cut-off and hence there will not be any resonance, but in reality it is impossible to have a perfect cone, since the vertex will always terminate with a finite dimension (not a point). I explored some time ago some geometries, and it looks like there is plenty of room to explore truncated cones that terminate at different distances from the cone vertex.

Yes but only when observed from a reference frame. Traveller's accelleration (from travellers PoV) reduces as a square root and that is not asymptotically (the limit you stated). If it were, speed from the traveller's frame of reference could never grow toward infinity, which it can occording to GR.

The limit on acceleration in the cavity frame of reference will always be less than that given in the formula if the cavity (and power system) has finite mass. The "g" there is indicative of what a self-accelerating wave packet of those dimensions would see if there was a zero-mass cavity.

while realizing my knowledge of electromagnetism falls short compared to level that is discussed here, i do have a question about that interesting idea on momentum transfer of the waves :

-with the law on conservation of energy in the back of my head -

How can the momentum transfer of a wave be bigger then the energy contained in a photon, as seen in a pure photon rocket ? I believe calculations showed the forces observed in the frustum are many times (100? 1000?) greater then what a photon rocket would be able to produce...

Due to the duality of microwave being a photon particle and a wave at the same time, shouldn't the energy contained in a wave/particle be the same?

Is it because for a photon rocket only a small portion of that energy is used for kinetic motion, while in the momentum transfer a greater part of the energy is transferred?

while realizing my knowledge of electromagnetism falls short compared to level that is discussed here, i do have a question about that interesting idea on momentum transfer of the waves :

-with the law on conservation of energy in the back of my head -

How can the momentum transfer of a wave be bigger then the energy contained in a photon, as seen in a pure photon rocket ? I believe calculations showed the forces observed in the frustum are many times (100? 1000?) greater then what a photon rocket would be able to produce...

Due to the duality of microwave being a photon particle and a wave at the same time, shouldn't the energy contained in a wave/particle be the same?

Is it because for a photon rocket only a small portion of that energy is used for kinetic motion, while in the momentum transfer a greater part of the energy is transferred?

Concerning Todd's formulation, I attach below his reply that was posted in another thread, that may also be of help concerning the above question:

COM=conservation of momentumGR=General Relativity

His answer has to do with the "gravitational field" inside the cavity, which can have different levels of energy :(in one post he suggested that the experimenters should post a label on the frustum reading "Gravitational Field Inside")

Not yet... I'm just now coming to grips with this myself. My light-bulb went off when I realized if the frequency of the microwaves is very close to the cut-off frequencies, then the speed of light will have a very large gradient inside the Frustum. Relative to the "traveling" waves (photons) attempting to move at the speed of light from end to end. When they approach the small end, their wavelength is squeezed by the reduced group velocity. Momentum depends on wavelength;

p = h/lambda

wavelength depends on velocity, and v_g is a variable inside the frustum.

That is where the momentum is coming from. Inside the Frustum, relative to the traveling waves you have an accelerated reference frame, into which you are injecting photons that are affected by this manufactured "gravitational" field, that must be compensated for by moving the Frustum.

I'll see what I can come up with for a formal equation, but I've got a day job. As for @ppnl, you will never get a Newtonian-type COM equation out of this. The two frames are the Frustum, and the frame of the moving photons inside it. The acceleration is caused by the geometry of the waveguide or a variable refractive index, i.e. the GR or PV Interpretation lead to the same result.

Todd D.

Well I certainly agree that You will never get Newtonian-type COM equation out of this. That's what makes it a violation of COM. Hard and simple. You are free to develop a theory that does not conserve momentum but you should call it what it is.

And I don't care what frames are inside the thing. Frames of reference are mathematical fictions. They don't exist. I should not need two frames of reference but only one and it is chosen only for convenience not truth. Any frame should do. Again you are free to develop a theory with a preferred frame that is real but you need to know that that is what you are doing and tell people that that is what you are doing.

If you insist on using Newtonian mechanics, then you will never understand COM in terms of General Relativity. I have not formulated a "new" theory, I'm using GR correctly. If you learn how to do COM in GR, then you would have no trouble seeing that this does indeed conserve momentum. The fact that you "don't care what is inside" is what is preventing you from learning. The "gravitational" field effect of a variable speed of light, acting on the photons inside the Frustum is what makes it move. If you neglect that it has a gravitational field inside it, then you neglect the very essence of how it works and why momentum is conserved. If you want to neglect GR and "believe" COM is violated, then that is your prerogative.

As for why it was not discovered already, I'm kicking myself in the a** for not thinking of this setup 10 years ago when I realized we can mimic gravity over a limited bandwidth with much less energy than over the full bandwidth of all light and matter waves. When my colleague and I wrote our EGM III paper, we had a resonant cavity like this in mind, but we didn't consider the taper.

Apologies to all. I thought I had read all the older forum pages. Seems I missed quite a few. Just about finished.

What I did find and confirmed via a search is that Shawyer's latest revelation, in an email to Mullerton, was that the Flight Thruster end plates WERE SHAPED seems to have missed making the headlines.

I did read there was quite a bit of speculation during the time the Flight Thruster dimensions were being worked out as to whether the end plates were flat or shaped.

So how we have it from Shawyer himself, the Flight Thruster was designed to have a high Q (narrow bandwidth), use a narrow band RF generator and have shaped end plates. Seems we finally know for sure why the end plates were so thick.

The EM Drive will sit on top of but not connected to one end of a balance beam. On the other will be an adjustable counter balance mass. Very low stiction bearings will be used.

The EM Drive end of the balance beam will sit on top of but not connected to a digital load cell with a 0.01g resolution / 0.5kg max and be connected via USB to a laptop running data logger software. Would like more resolution, will see how the budget goes.

The counter balance will be adjusted to produce a down force on the load cell of 0.25kg when the EM Drive is unpowered so to bias the load cell into the middle of it's range.

The frequency and power adjustable RF source will be connected to the EM Drive by a free floating length of coax with SWR matching capability and to the laptop via USB connector. Control of frequency and power will be via software on the laptop.

The idea is to keep this KISS and stay as close to the 1st Shawyer test setup that also used vertical orientation of the EM Drive.

Based on achieving 10mN/kW (~1gf/kW) performance, the desired 0.1gf (10x load cell resolution) will need the application of 100W of RF power.

Desire is to use common 2.4GHz narrow band WiFi based signal generators which can be smoothly varied in frequency and power output to find optimal cavity frequency and energy loading.

As this is a narrow band RF signal, ideally the end caps should be spherical to eliminate end plate variable phase change and to get a much better cavity Q. But being a realist and KISS engineer, who hates to reinvent the wheel, will start with simpler flat plates and will follow the excellent work of Mullerton.

Comments most welcome

One possible problem I see with your proposed experiment is the coiled coax. There will always be a significant error force from that and there is no simple way of cancelling it out. Maybe a telescoping waveguide feed would solve that problem. The load cell will also be in jeopordy. Too much imbalance will crush it.

The tapered frustum's sole purpose is to create a standing EM wave of specific frequency. As far as I remember, a standing wave could also be interpreted as a confined particle in quantum mechanics. Is there any possibilty that the standing waves within the cavity resemble dynamically created exotic matter that shows weird behavior when interacting with the 'normal' matter that the EM-drive is made of?

This is at least similar to some claims made by Dr white. However I am not sure I have properly understood what he meant when he said these things are doing essentially the same thing the QVPT does and (I think?) maybe he said the QVPT and the Warp Interferometry test article got it's negative energy from the vacuum. Anyhow it may be that your supposition aligns with Dr White but i am not completely sure I understand it.